manual derivatives done using the definition 45 videos

Derivatives of Exponential Functions
Calculus The Derivative
How to use the definition of the derivative to find a derivative formula for exponential functions.
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The Definition of the Derivative
Calculus The Derivative
How to define the derivative of a function at a point x=a.
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Computing Definite Integrals using Substitution
Calculus The Definite Integral
How to evaluate definite integrals using the method of substitution.
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The Derivative Function
Calculus The Derivative
How to define the derivative function f'(x).
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Derivatives of Polynomial Functions
Calculus The Derivative
How to compute the derivative of a polynomial function using two properties of the derivative.
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Derivatives of Power Functions
Calculus The Derivative
How to determine the derivative of a power function.
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Derivative Notation
Calculus The Derivative
How to recognize and use Newton's and Leibniz's notation for the derivative.
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Derivatives of Logarithmic Functions
Calculus The Derivative
How to infer the derivative of the natural log function using a calculator investigation.
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Derivatives of Linear Functions
Calculus The Derivative
How to determine the derivative of a linear function.
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Definite Integrals and Area
Calculus The Definite Integral
How to use definite integrals to find the area between a curve or under a curve.
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Definition of Antiderivatives
Calculus Antiderivatives and Differential Equations
How to define an antiderivative.
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Optimization Using the First Derivative Test
Calculus Applications of the Derivative
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.

Optimization Using the Second Derivative Test
Calculus Applications of the Derivative
How to compute the average velocity of an object moving in one dimension from a graph of its position vs. time.

Definite Integrals As Net Change
Calculus The Definite Integral
How to use the fundamental theorem of calculus to compute the net change of a quantity.
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Curve Sketching with Derivatives
Calculus Applications of the Derivative
How to evaluate the limit of a function using continuity.

The Fundamental Theorem of Calculus
Calculus The Definite Integral
How to use the fundamental theorem of calculus to evaluate a definite integral.
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Approximating Area Using Rectangles
Calculus The Definite Integral
How to approximate the area under a curve using rectangles.
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The First Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to use an algebraic approach to find onesided limits of a rational function, and how these limits can be used to find a vertical asymptote.

Definition of Indefinite Integrals
Calculus Antiderivatives and Differential Equations
How to define an indefinite integral.
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Antidifferentiation
Calculus Antiderivatives and Differential Equations
How to find an antiderivative of a function.
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